Refraction Traveltime Tomography Based on Adjoint State Techniques

Taillandier, Cédric; Noble, Mark; Chauris, Hervé; Podvin, Pascal; Calandra, Henri; Guilbot, J.

doi:10.3997/2214-4609.201401765

Cited by 3 publications

(1 citation statement)

References 5 publications

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“…Among these finite-difference eikonal solvers, the first-order fast marching and the first-order fast sweeping methods have proved to be unconditionally stable. Furthermore, related to the work in [46,47], fast-sweeping-based eikonal solvers have been successfully used in isotropic transmission traveltime tomography in [25], and the resulting method is robust; this method has been further developed in [58,57] for three-dimensional practical data.…”

Section: Introductionmentioning

confidence: 99%

An adaptive phase space method with application to reflection traveltime tomography

et al. 2011

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In this work, an adaptive strategy for the phase space method for traveltime tomography (Chung et al 2007 Inverse Problems 23 309-29) is developed. The method first uses those geodesics/rays that produce smaller mismatch with the measurements and continues on in the spirit of layer stripping without defining the layers explicitly. The adaptive approach improves stability, efficiency and accuracy. We then extend our method to reflection traveltime tomography by incorporating broken geodesics/rays for which a jump condition has to be imposed at the broken point for the geodesic flow. In particular, we show that our method can distinguish non-broken and broken geodesics in the measurement and utilize them accordingly in reflection traveltime tomography. We demonstrate that our method can recover the convex hull (with respect to the underlying metric) of unknown obstacles as well as the metric outside the convex hull.

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Section: Introductionmentioning

confidence: 99%

An adaptive phase space method with application to reflection traveltime tomography

et al. 2011

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Higher-order schemes for 3D first-arrival traveltimes and amplitudes

2012

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In the geometrical-optics approximation for the Helmholtz equation with a point source, traveltimes and amplitudes have upwind singularities at the point source. Hence, both first-order and higher-order finite-difference solvers exhibit formally at most first-order convergence and relatively large errors. Such singularities can be factored out by factorizing traveltimes and amplitudes, where one factor is specified to capture the corresponding source singularity and the other factor is an unknown function smooth near the source. The resulting underlying unknown functions satisfy factored eikonal and transport equations, respectively. A third-order Lax-Friedrichs scheme is designed to compute the underlying functions. Thus, highly accurate first-arrival traveltimes and reliable amplitudes can be computed. Furthermore, asymptotic wavefields are constructed using computed traveltimes and amplitudes in the WKBJ form. Two-dimensional and 3D examples demonstrate the performance of the proposed algorithms, and the constructed WKBJ Green’s functions are in good agreement with direct solutions of the Helmholtz equation before caustics occur.

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3-D Refraction Traveltime Tomography Algorithm Based on Adjoint State Techniques

Taillandier¹,

Noble²,

Calandra³

et al. 2008

70th EAGE Conference and Exhibition Incorporating SPE EUROPEC 2008

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Classical 3-D refraction traveltime tomography algorithms may suffer from computational limitations due to the large datasets that come from current seismic acquisition surveys. To overcome these issues, we suggest a 3-D refraction tomography algorithm based on adjoint state techniques to derive the gradient of the traveltime misfit function. We use the Eikonal equation for the forward modelling, and iterate with a conjugate gradient method. A 3-D synthetic example with a realistic size acquisition demonstrates the efficiency and the great potential of the adjoint state method for 3-D applications of refraction tomography.

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Refraction Traveltime Tomography Based on Adjoint State Techniques

Cited by 3 publications

References 5 publications

An adaptive phase space method with application to reflection traveltime tomography

An adaptive phase space method with application to reflection traveltime tomography

Higher-order schemes for 3D first-arrival traveltimes and amplitudes

3-D Refraction Traveltime Tomography Algorithm Based on Adjoint State Techniques

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